Finger SQUID qubit device

ABSTRACT

A finger SQUID qubit device and method for performing quantum computation with said device is disclosed. A finger SQUID qubit device includes a superconducting loop and one or more superconducting fingers, wherein the fingers extend to the interior of said loop. Each finger has a mesoscopic island at the tip, separated from the rest of the finger by a Josephson junction. A system for performing quantum computation with the finger SQUID qubit device includes a mechanism for initializing, entangling, and reading out the qubits. The mechanism may involve passing a bias current across the leads of the superconducting loop and a mechanism for measuring a potential change across the leads of the superconducting loop. Furthermore, a control system includes a mechanism for addressing specific qubits in a quantum register of finger SQUID devices.

RELATED APPLICATIONS

[0001] This application is a divisional of U.S. application Ser. No.______ {Attorney Docket Number M-12305 US}, by the same inventors, whichis herein incorporated by reference in its entirety.

BACKGROUND

[0002] 1. Field of the Invention

[0003] This invention relates to quantum computing and, in particular,to superconducting quantum computing systems.

[0004] 2. Description of Related Art

[0005] Research on what is now called quantum computing traces back toRichard Feynman. See, e.g., R. P. Feynman, Int. J. Theor. Phys. 21, 467(1982). He noted that quantum systems are inherently difficult tosimulate with classical (i.e., conventional, non-quantum) computers, butthat this task could be accomplished by observing the evolution ofanother quantum system. In particular, solving a theory for the behaviorof a quantum system commonly involves solving a differential equationrelated to the system's Hamiltonian. Observing the behavior of thesystem provides information regarding the solutions to the equation.

[0006] Further efforts in quantum computing were initially concentratedon building the formal theory or on “software development” or extensionto other computational problems. Discovery of the Shor and Groveralgorithms were important milestones in quantum computing. See, e.g., P.Shor, SIAM J. of Comput. 26, 1484 (1997); L. Grover, Proc. 28th STOC,212 (ACM Press, New York, 1996), which is hereby incorporated byreference in its entirety; and A. Kitaev, LANL preprintquant-ph/9511026, which is hereby incorporated by reference in itsentirety. In particular, the Shor algorithm permits a quantum computerto factorize large natural numbers efficiently In this application, aquantum computer could render obsolete all existing “public-key”encryption schemes. In another application, quantum computers (or even asmaller-scale device such as a quantum repeater) could enable absolutelysafe communication channels where a message, in principle, cannot beintercepted without being destroyed in the process. See, e.g., H. J.Briegel et al., preprint quant-ph/9803056 and references therein, whichis hereby incorporated by reference in its entirety. Showing thatfault-tolerant quantum computation is theoretically possible opened theway for attempts at practical realizations. See, e.g., E. Knill, R.Laflamme, and W. Zurek, Science 279, 342 (1998), which is herebyincorporated by reference in its entirety.

[0007] Quantum computing generally involves initializing the states of Nqubits (quantum bits), creating controlled entanglements among them,allowing these states to evolve, and reading out the states of thequbits after the evolution. A qubit is conventionally a system havingtwo degenerate (i.e., of equal energy) quantum states, with a non-zeroprobability of being found in either state. Thus, N qubits can define aninitial state that is a combination of 2^(N) classical states. Thisinitial state undergoes an evolution, governed by the interactions thatthe qubits have among themselves and with external influences. Thisevolution of the states of N qubits defines a calculation or, in effect,2^(N) simultaneous classical calculations. Reading out the states of thequbits after evolution is complete determines the results of thecalculations.

[0008] Several physical systems have been proposed for the qubits in aquantum computer. One system uses molecules having degeneratenuclear-spin states. See N. Gershenfeld and I. Chuang, “Method andApparatus for Quantum Information Processing,” U.S. Pat. No. 5,917,322,which is hereby incorporated by reference in its entirety. Nuclearmagnetic resonance (NMR) techniques can read the spin states. Thesesystems have successfully implemented a search algorithm, see, e.g., M.Mosca, R. H. Hansen, and J. A. Jones, “Implementation of a quantumsearch algorithm on a quantum computer,” Nature 393, 344 (1998) andreferences therein, which is hereby incorporated by reference in itsentirety, and a number-ordering algorithm, see, e.g., L. M. K.Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, R. Cleve, and I. L.Chuang, “Experimental realization of order-finding with a quantumcomputer,” preprint quant-ph/0007017 and references therein, which ishereby incorporated by reference in its entirety. (The number-orderingalgorithm is related to the quantum Fourier transform, an essentialelement of both Shor's factoring algorithm and Grover's algorithm forsearching unsorted databases.) However, expanding such systems to acommercially useful number of qubits is difficult. More generally, manyof the current proposals will not scale up from a few qubits to the10²˜10³ qubits needed for most practical calculations.

[0009] Further, current methods for entangling qubits are susceptible toloss of coherence. Entanglement of quantum states of qubits can be animportant step in the application of quantum algorithms. See forexample, P. Shor, SIAM J. of Comput., 26:5, 1484-1509 (1997), which ishereby incorporated by reference in its entirety. Current methods forentangling phase qubits require the interaction of the flux in each ofthe qubits, see Yuriy Makhlin, Gerd Schon, Alexandre Shnirman, “Quantumstate engineering with Josephson-junction devices,” LANL preprint,cond-mat/0011269 (November 2000), which is hereby incorporated byreference in its entirety. This form of entanglement is sensitive to thequbit coupling with surrounding fields, which cause decoherence and lossof information.

[0010] As discussed above, currently proposed methods for readout,initialization, and entanglement of a qubit involve detection ormanipulation of magnetic fields at the location of the qubit, which makethese methods susceptible to decoherence and limits the overallscalability of the resulting quantum computing device. Thus, there is aneed for an efficient quantum register where decoherence and othersources of noise is minimized but where scalability is maximized.

SUMMARY OF THE INVENTION

[0011] In accordance with the present invention, a quantum register ispresented. A quantum register according to the present inventionincludes one or more finger SQUID qubit devices.

[0012] A finger SQUID qubit device according to an embodiment of thepresent invention can include a superconducting loop and asuperconducting finger, wherein the superconducting finger extends fromthe superconducting loop towards the interior of the superconductingloop. The superconducting loop may have multiple branches. Each branchmay have a Josephson junction. The Josephson junction may be a grainboundary junction. The finger SQUID qubit device may have leads capableof conducting current to and from the superconducting loop. The leadsmay be capable of conducting supercurrent.

[0013] When structures are referred to as “superconducting” herein, theyare fabricated from a material capable of superconducting and so maysuperconduct under the correct conditions. For example, thesuperconducting loop and superconducting finger may be fabricated from ad-wave superconductor and so will superconduct under appropriatephysical conditions. For example, the superconducting loop and fingerwill superconduct at an appropriate temperature, magnetic field, andcurrent. However, the “superconducting loop” will not superconduct underother physical conditions. For example, when the temperature is toohigh, the superconducting loop will not be in a superconducting state.Additionally, structures such as superconducting SETs and othersuperconducting switches mentioned herein are capable of superconductingunder appropriate physical conditions.

[0014] A device in accordance with an embodiment of the inventiongenerally operates at a temperature such that thermal excitations in thesuperconducting crystal lattice are sufficiently suppressed to performquantum computation. In some embodiments of the invention, such atemperature can be on the order of 1K or less. In some other embodimentsof the invention, such a temperature can be on the order of 50 mK orless. Furthermore, other dissipative sources, such as magnetic fieldsfor example, should be minimized to an extent such that quantumcomputing can be performed with a minimum of dissipation anddecoherence.

[0015] The material capable of superconducting used in embodiments ofthe invention may be a material that violates time-reversal symmetry.For example, a d-wave superconductor may be used. For example, thed-wave superconductors YBa₂Cu₃O_(7−x), Bi₂Sr₂Ca_(n−1)Cu_(n)O_(2n+4),Tl₂Ba₂CuO_(6+x), and HgBa₂CuO₄ may be used.

[0016] According to some embodiments of the present invention, thesuperconducting finger includes a Josephson junction, such that amesoscopic island is separated from the rest of the superconductingfinger by the junction.

[0017] For the Josephson junctions in the branches or the finger, theorientation of the superconducting order parameter on one side of theJosephson junction may be different from the orientation of thesuperconducting order parameter on the other side of the Josephsonjunction. For example, the orientation of the superconducting orderparameter in the region above the Josephson junction may be rotatedapproximately 45 degrees with respect to the orientation of thesuperconducting order parameter below the Josephson junction. Othernon-zero misorientations may be used to form a grain boundary Josephsonjunction. The orientation of the superconducting order parameter in theregion above the Josephson junction may be rotated with respect to theorientation of the grain boundary. The orientation of thesuperconducting order parameter in the region below the Josephsonjunction may be rotated with respect to the orientation of the grainboundary.

[0018] The orientation of the superconducting order parameter is relatedto the orientation of the crystal lattice of the superconductor.Therefore, the orientation of the superconducting order parameter isgenerally controlled by controlling the orientation of the crystallattice. For example, bi-epitaxial fabrication methods can be used toachieve the desired orientation of the superconducting order parameterin regions adjacent to the grain boundary. Alternately, bi-crystalfabrication methods may be used to achieve the desired orientation ofthe superconducting order parameter in regions adjacent to the grainboundary.

[0019] In a qubit device as presented in embodiments of the currentinvention, the superconducting finger, including the mesoscopic islandregion, forms a qubit as explained below, and the surroundingsuperconducting loop allows interaction with and control of the qubit.The loop and finger together, then, can be referred to as the qubitdevice.

[0020] If the order parameter in a first region of the loop, from whichthe finger extends, has a phase of Φ, a phase Φ±ΔΦ is accumulated in theorder parameter across the Josephson junction in the finger. The sign ofthe phase change depends on the direction of circulation of the groundstate supercurrent. The qubit has two bistable phase states,corresponding to the change in phase +ΔΦ or −ΔΦ of the order parameteracross the Josephson junction in the finger. Therefore, the region ofqubit device including the finger and the region of the loop from whichthe finger extends can then be referred to as the qubit. Additionally,the two bi-stable phase states form the basis states of the qubit can bereferred to as the |+ΔΦ> and |−ΔΦ> states, with measurable qubit phasechange values of +ΔΦ and −ΔΦ. For operation as a qubit, these states arereferred to as the basis states |0> and |1>.

[0021] Although the measurable values of the qubit phase change areequal to +ΔΦ or −ΔΦ, in a quantum computing device the qubit phase isgenerally not directly measured. The term “measurable value” here refersto the quantum mechanical use of the term, where a measurable value is aphysical attribute of a system that can be described by an operator inthe system's Hilbert space (such as energy, position or momentum). Inmaking an actual measurement, a current may be provided through a qubitdevice and a resulting voltage across the qubit device will be measured.The measured voltage will depend on the state of the qubit. That is, themeasured voltage will be different if the qubit is in the basis statecorresponding to a measurable value of the qubit phase difference of +ΔΦthan if the qubit is in the basis state corresponding to a measurablevalue of the qubit phase difference of −ΔΦ.

[0022] In some embodiments of the current invention, a control system isincluded. The control system may provide current to the superconductingleads of a qubit device as described above. The control system may alsomeasure a voltage change across the leads, may convert a measuredvoltage change to a qubit value, may store the qubit value, and/or maystore the measured voltage change. The qubit value corresponds to one ofthe two qubit basis states described above, but in this example thequantities +ΔΦ and −ΔΦ are not directly measured. Instead, the qubitvalue may be stored as a voltage, as a 1 or a 0, or as some otherparameter.

[0023] In some embodiments of the invention, the orientation of thegrain boundary forming the junction can be tilted with respect to theorientation of the branches of the superconducting loop. This can alterthe phase of the superconducting ground state beyond the shift caused bythe misorientation of the superconductor crystal lattice with thecorresponding grain boundary. Alternately, one or more of the branchesof the superconducting loop can be tilted with respect to theorientation of the grain boundaries forming the grain boundary Josephsonjunctions.

[0024] Further, the branches or the grain boundaries forming theJosephson junctions in the branches can have a different tilt angle withrespect to one another, such that the junctions in each branch cancorrelate with a different ground state phase difference. Again, thisground state phase difference may be accompanied by a ground state phasedifference caused by the misorientation of the superconductor crystallattice with the corresponding grain boundary. Furthermore, said groundstate phase difference across the junctions in the branches of thesuperconducting loop can be different from the ground state phasedifference across the junction isolating the island on thesuperconducting finger. The ground state phase difference can depend onthe direction of the grain boundary with respect to the orientation ofthe superconducting order parameter above and below the grain boundaryor on direction of the grain boundary with respect to the branch.

[0025] In some embodiments of the invention, a link may be providedbetween the superconducting loop and the mesoscopic island of a qubitdevice as described above. The link may include a switching mechanism.The switching mechanism may be a coherent switching mechanism such as aparity key or superconducting SET.

[0026] In some embodiments of the invention, a link may be providedbetween the mesoscopic island of a qubit device as described above and aground. The link may include a switching mechanism. The switchingmechanism may be a coherent switching mechanism such as a parity key orsuperconducting SET.

[0027] In some embodiments of the quantum register, the magnitude of ΔΦmay differ between qubit devices depending on the characteristics ofeach qubit device. Such a difference does not affect the ability of thequbit devices to be used in quantum computing. Further, by controllingthe fabrication of the qubit devices so that differences between devicesare minimal, the magnitude of the qubit phase may only slightly varyamong devices. However, even though the magnitude of the qubit phasecorresponding to one of the qubit basis states may differ among devices,for each particular qubit device there are doubly degenerate basisstates as described above which correspond to two measurable values ofqubit phase.

[0028] In some embodiments of the current invention, a quantum registerincludes multiple qubit devices. Each qubit device may include one ormore qubits. In an embodiment where a quantum register includes a firstqubit device and a second qubit device, the first qubit device may becoupled to the second qubit device by providing a coupling link betweena mesoscopic island of the first device and a mesoscopic island of asecond device. The coupling link can include a coupling switch, suchthat when the coupling switch is in the closed position it conductscurrent. In some embodiments, the coupling link can coherently conductsupercurrent. The coupling switch may be a superconducting SET or aparity key.

[0029] In some embodiments of the invention, a quantum register includesone or more superconducting loops. Each superconducting loop may includemultiple fingers extending from the loop toward the interior of theloop. Each finger may include a Josephson junction separating amesoscopic island from the rest of the finger.

[0030] In some embodiments of the invention, a quantum register mayinclude a plurality of superconducting loops, where each loop has afinger extending from the loop towards its interior. Each finger mayhave a Josephson junction separating a mesoscopic island from the restof the finger.

[0031] In some embodiments of the invention, a method of performing acalculation with a quantum computer may include providing a quantumregister. The quantum register may include multiple qubit devices asdescribed above. The method of performing a calculation may includeinitializing the qubit devices to one of the qubit basis states. Themethod may include coupling one of the qubit devices to another of thedevices, so that the quantum states of each of the qubit devices areentangled. The method may include reading the result of the calculation.Reading the result of the calculation may include collapsing the qubitwavefunction into one of its basis states. The method may includestoring the results of the calculation in a memory.

[0032] Embodiments of the invention can include a method forinitializing a qubit. The method can include providing a qubit device asdescribed above, where the qubit has two basis states, ⊕αΔΦ> and |−ΔΦ>.The method can include initializing the qubit by setting the qubit phaseto one of the two ground state values. The state of the qubit can belocalized to a single ground state by connecting the mesoscopic islandof the qubit device to a ground. Alternately, the qubit state can be setby coupling the mesoscopic island of the qubit device to thesuperconducting loop of the qubit device. The qubit state may be set bydriving a bias current across the leads of the superconducting loop.

[0033] Embodiments of the invention can include performing anentanglement operation. An entanglement operation may be performed bycoupling two or more qubit devices. For example, an entanglementoperation may be performed by providing a first qubit device and asecond qubit device as described above, then coupling the first qubitdevice to the second qubit device. The first qubit device may be coupledto the second qubit device by providing a link between the mesoscopicisland of the first qubit device and the mesoscopic island of the secondqubit device. The link may include a coherent superconducting switch.The coherent superconducting switch can be a superconducting SET or aparity key. In another embodiment, the first qubit device can be coupledto the second qubit device by providing a superconducting loop betweenthe first qubit device and the second qubit device. The superconductingloop can include a switch such that when the switch is closed thesuperconducting loop is inductively coupled to the first qubit and thesecond qubit.

[0034] Multiple qubits may be entangled by coupling as described above.For example, a first qubit device may be coupled to a second qubitdevice as described above. Additionally, the first qubit device may becoupled to a third qubit device. The first qubit device may be coupledto the second qubit device and the third qubit device at the same time.The multiple qubit devices may be arranged in a one-dimensional array, atwo-dimensional array, or a three-dimensional array.

[0035] Some embodiments of the invention include a method for performinga bias operation on a qubit. The method can include providing a qubitdevice as described above. The method can further include linking themesoscopic island of the qubit device to the superconducting loop of thequbit device. The linking can be accomplished using a coherent switchingmechanism. The coherent switching mechanism can be a superconducting SETor a parity key.

[0036] In some embodiments of the current invention, a method forperforming a bias operation can include providing a qubit device asdescribed above. The method can include driving a bias current acrossthe leads of the qubit device. Driving the current in a first directioncan bias the qubit to one of the two qubit basis states, while drivingthe current in the opposite direction can bias the qubit to the other ofthe two qubit basis states.

[0037] In some embodiments of the current invention, a method of readingout the state of a qubit device can include providing a qubit device asdescribed above. The method may include coupling the mesoscopic islandof the qubit device to the superconducting loop of the qubit device. Themethod may further include driving a bias current through the leads ofthe qubit device. The method may include measuring a voltage changeacross the leads of the qubit device. The method may include storing themeasured voltage change or storing a qubit value corresponding to themeasured voltage change in a memory.

[0038] In some embodiments of the current invention, a method of readingout the state of a qubit includes providing a qubit device as describedabove. The method may further include grounding the qubit device. Themethod may include applying a current across the leads of the qubitdevice and measuring a voltage change across the leads of the qubitdevice, where the voltage change may differ depending on which of thetwo basis states the qubit is in. The method may include storing themeasured voltage change or storing a qubit value corresponding to themeasured voltage change in a memory. The qubit value may be a voltage, a0 or a 1, or some other parameter that represents the basis state of thequbit, which is not directly measured in this example.

[0039] In some embodiments, a method of grounding a qubit includesproviding a qubit device as described above. The method may furtherinclude connecting the mesoscopic island of the qubit device to aground.

[0040] In some embodiments, a method of grounding a qubit deviceincludes providing a qubit device as described above. The method mayfurther include driving a current across the leads of the qubit device.

[0041] In some embodiments of the invention, a method for initializingthe state of a quantum register may include initializing the state ofeach qubit in the register. The method may further include grounding allof the qubits in the quantum register. The method may further includedriving a current across the leads of each of the qubit devices, inparallel or in series.

[0042] In some embodiments of the invention, a method for applyingquantum gates using the quantum register may include performing biasoperations or entanglement operations on one or more qubits in parallelor in series.

[0043] In some embodiments of the invention, a method for reading outthe state of a quantum register may include performing a readoutoperation on each of the qubits in the quantum register in parallel orin series.

[0044] These and other embodiments are further described below withrespect to the following figures.

DESCRIPTION OF THE FIGURES

[0045]FIG. 1 illustrates a plan view of a Permanent ReadoutSuperconducting Qubit (PRSQ) device;

[0046]FIG. 2 illustrates a plan view of an embodiment of a finger SQUIDqubit device according to the present invention;

[0047]FIGS. 3A through 3D illustrate a method of fabricating a fingerSQUID qubit device;

[0048]FIG. 4 illustrates a plan view of another embodiment of a fingerSQUID qubit device according to the present invention;

[0049]FIG. 5 illustrates a plan view of a quantum register in accordancewith some embodiments of the invention;

[0050]FIG. 6 illustrates a plan view of a control system coupled to aquantum register such as that shown in FIG. 5;

[0051]FIG. 7 illustrates a plan view of a plurality of quantum registersin accordance with another embodiment of the invention;

[0052]FIG. 8 illustrates a plan view of a plurality of quantum registersin accordance with another embodiment of the invention;

[0053]FIG. 9 illustrates a plan view of a quantum register in accordancewith another embodiment of the invention;

[0054]FIG. 10 illustrates a plan view of a control system for a qubitaccording to an embodiment of the present invention;

[0055]FIG. 11 illustrates a plan view of a quantum processor accordingto the present invention;

[0056]FIG. 12 illustrates a plan view of an RF-SET voltmeter.

[0057]FIG. 13 illustrates a quantum register in accordance with anembodiment of the invention.

DETAILED DESCRIPTION

[0058] The following is a glossary of terms used in this application.Although these terms are well known in the art of quantum computing, theglossary is provided to facilitate understanding of the application.

[0059] Basis states: The states of the quantum mechanical system beingused for storing information.

[0060] Bias operation: An operation performed on a qubit in a quantumcomputing system by energetically favouring one basis state of a qubitover the other.

[0061] Bi-crystal fabrication: Formed by connecting together twocrystals with a predetermined misorientation between them.

[0062] Bi-epitaxial fabrication: Formed by providing a seed layer tocontrol the crystal orientation of a layer grown on the seed layerversus off the seed layer.

[0063] Bulk superconductor: A region of superconducting material with asize such that the phase of the order parameter is fixed throughout theregion.

[0064] Coherent superconductor switch: a switch that controllablyconducts supercurrent, such that the phase of the supercurrent enteringthe switch is the same as the phase of the supercurrent leaving theswitch; see parity key.

[0065] Collapsing the wavefunction: To remove the probabilistic natureof the wavefunction, leaving the quantum system to occupy a singlestate. This can be accomplished by measuring the system; for example, bygrounding a qubit.

[0066] Conventional superconductor: a superconducting material where thesuperconducting order parameter exhibits s-wave symmetry and has ametallic normal state.

[0067] Coulomb energy: charging energy E_(c)=e²/2C of a single electronfor a Josephson junction of a given capacitance (energy gained byplacing an additional single electron on a device of a givencapacitance).

[0068] Critical current: The current above which dynamical processesoccur in a Josephson junction. Such dynamical processes result inquasiparticle excitation in the current flow.

[0069] D-wave superconductor: a superconducting material where thesuperconducting order parameter exhibits d-wave pairing symmetry.

[0070] Decoherence: Loss of information in a quantum mechanical systemcaused by interaction with an environment.

[0071] Entanglement of quantum states: Non-local coupling of two of morequbits, whereby affecting one qubit affects all qubits it is entangledwith.

[0072] Entanglement operation: An operation performed in a quantumcomputing system that entangles the wavefunctions of two or more qubits.

[0073] Grain boundary: A boundary separating two regions of materialhaving different crystal lattice orientations.

[0074] Heterostructure junction (S/D heterostructure junction):Josephson junction with a conventional superconductor on one side and anunconventional superconductor on the other side. Such a junction can beformed in the plane of the substrate (a-b) or in a plane normal theplane of the substrate (c-axis).

[0075] Josephson energy: the energy E_(J) corresponding to the entranceor exit of one Cooper pair by tunneling through the Josephson junction.

[0076] Josephson junction (tunnel junction): a junction between twosuperconductors, where the superconducting order parameter is suppressedat the junction.

[0077] Measurable value: Any physical attribute of a system that can bedescribed by an operator in the system's Hilbert space (such as energy,position or momentum).

[0078] Mesoscopic: Between microscopic and macroscopic. A mesoscopicdevice indicates a device with physical dimension of physically smallsize such that some phenomena observed on the structure require quantummechanical explanation. Mesoscopic typically refers to structures on theorder of 10⁻⁶ m in extent.

[0079] Parity key: A switch that controllably permits the coherent flowof Cooper pairs, while suppressing the flow of quasiparticles; seecoherent superconductor switch.

[0080] Plasma frequency: the frequency of plasma oscillations in theJosephson junction, which is a function of the Coulomb energy and theJosephson energy.

[0081] Quantum computing: computing accomplished using quantummechanical effects of physical systems that exhibit quantum mechanicalbehaviour.

[0082] Quantum gate: an information transformation gate that can beapplied to the quantum information of a quantum computing system;analogous to the classical gates which include AND, OR, gates as well asothers.

[0083] Quantum register: an array of one or more qubits, capable ofstoring multiple pieces of quantum information. A quantum register canalso manipulate the information in the qubits that it contains.

[0084] Qubit: a physical system that is restricted to two or morequantum states for storing information, where information is containedin the quantum state of the system. The quantum states of the qubit canbe made degenerate, having equal energy.

[0085] Qubit tunneling amplitude: the frequency of tunneling between thebasis states of a qubit.

[0086] Refocusing techniques: techniques which can be applied tomaintain the correct state in the quantum register.

[0087] SQUID: a superconducting quantum interference device; usually aloop of superconducting material including one or two Josephsonjunctions.

[0088] Superconducting order parameter: a property of a superconductingmaterial that describes the behaviour of charge carriers in thesuperconducting material.

[0089] Superconducting single electron transistor: A switch thatcontrollably allows the passage of current; where current includescharge carriers both in the superconducting state and not in thesuperconducting state.

[0090] Supercurrent: Flow of the superconducting condensate, which ismade up of charged particles formed from pairwise bound electrons,usually called Cooper pairs.

[0091] Superposition of states: A quantum mechanical state in whichthere is a non-zero probability of occupying more than one of the basisstates of the quantum mechanical system at a given time.

[0092] Time reversal symmetry: a function has time reversal symmetrywhen the same results are obtained when time runs forward as when timeruns backward.

[0093] Tunnel matrix operation: An operation performed on a qubit in aquantum computing system controlling the rate of oscillation betweenbasis states of the qubit.

[0094] Wavefunction: a probabilistic envelope that describes the quantummechanical state of a quantum object.

[0095] As stated above, when structures are referred to as“superconducting” herein, they are fabricated from a material capable ofsuperconducting and so may superconduct under the correct conditions.For example, the superconducting loop and superconducting finger may befabricated from a d-wave superconductor and so will superconduct underappropriate physical conditions. For example, the superconducting loopand finger will superconduct at an appropriate temperature, magneticfield, and current. However, the “superconducting loop” will notsuperconduct under other physical conditions. For example, when thetemperature is too high, the superconducting loop will not be in asuperconducting state. Additionally, structures such as superconductingSETs and other superconducting switches mentioned herein are capable ofsuperconducting under appropriate physical conditions.

[0096] A device in accordance with an embodiment of the inventiongenerally operates at a temperature such that thermal excitations in thesuperconducting crystal lattice are sufficiently suppressed to performquantum computation. In some embodiments of the invention, such atemperature can be on the order of 1K or less. In some other embodimentsof the invention, such a temperature can be on the order of 50 mK orless. Furthermore, other dissipative sources, such as magnetic fieldsfor example, should be minimized to an extent such that quantumcomputing can be performed with a minimum of dissipation anddecoherence.

[0097] A finger-SQUID phase qubit device according to the presentinvention includes a superconducting loop and a superconducting finger,where the finger extends towards the interior of the loop and includes aJosephson junction. The superconducting loop may have two or morebranches. The branches of the superconducting loop further includeJosephson junctions, a region in which the order parameter of thesuperconductor is suppressed, which allow the finger-SQUID qubit deviceto operate in an optimal regime for controlling the qubit.

[0098] For example, a superconducting loop may have two branches. Foreach of the two branches, the superconducting order parameter has afirst orientation in one region and a second orientation in anotherregion. The first orientation may differ from the second orientation,for example, by 45 degrees. Alternately, a non-zero misorientation otherthan 45 degrees may be used. At the boundary between the two regions, agrain boundary Josephson junction is formed. The superconducting orderparameter can undergo a phase change across the Josephson junction.Depending on the geometry of each of the branches and the grainboundary, the Josephson junction in each branch may cause the same phasechange in the superconducting ground state or the phase changes maydiffer among some or all of the Josephson junctions.

[0099] The Josephson junction in the finger of the qubit creates amesoscopic island. The size of the island and the parameters of theJosephson junction are chosen so that the addition of a single unit ofsuperconducting charge (a Cooper pair) to the island can be measured.The basis states of the qubit are determined in the following manner: ifthe order parameter in a first region of the loop, from which the fingerextends, has a phase of Φ, a phase Φ±ΔΦ is accumulated in the orderparameter across the Josephson junction in the finger, the sign of whichdepends on the direction of circulation of the ground state supercurrentat the Josephson junction. Therefore, the qubit can be said to have twobistable phase states, corresponding to the change in phase +ΔΦ or −ΔΦof the order parameter across the Josephson junction in the finger. Theportion of the qubit device including the first region in the loop fromwhich the finger extends and the finger can be referred to as the qubit.

[0100] Therefore, the bistable ground states of the device in the regionof the finger near the Josephson junction which separates the mesoscopicisland from the rest of the finger, can be used as the basis states of aqubit for quantum computation. Additionally, the two bi-stable phasestates forming the basis states of the qubit can be referred to as the|+ΔΦ> and |−ΔΦ> states, with qubit values corresponding to the phasedifference values of +ΔΦ and −ΔΦ respectively. The basis states of thequbit may, alternatively, be referred to as the |1> and |0> states. Then|+ΔΦ> may be designated as either the |1> state or the |0> state, and|−ΔΦ> may then be designated as the opposite state.

[0101] As stated previously, although the measurable values of the qubitphase change are equal to +ΔΦ or −ΔΦ, in a quantum computing device thequbit phase change is generally not directly measured. Instead, acurrent may be provided through a qubit device and a resulting voltageacross the qubit device will be measured. The measured voltage willdepend on which basis state the qubit occupies. That is, the measuredvoltage will be different if the qubit is in the basis statecorresponding to a measurable value of the qubit phase change of +ΔΦthan if the qubit is in the basis state corresponding to a measurablevalue of the qubit phase change of −ΔΦ.

[0102] The basis states of the qubit, |+ΔΦ> and |−ΔΦ>, correspond to twomeasurable values for the qubit phase change. During a quantumcalculation, the qubit state may not correspond to either of the basisstates but instead may be a superposition of the two basis states.However, measurement of the state of the qubit will collapse the qubitstate wavefunction to a single basis state.

[0103] The material of the finger-SQUID phase qubit may be anysuperconducting material that violates time reversal symmetry. Thed-wave superconductor YBa₂Cu₃O_(7−x), where x is between 0 and 0.6, isan example of a useful superconducting material. Additionally,Bi₂Sr₂Ca_(n−1)CuO_(2n+4), Tl₂Ba₂CuO_(6+x), and HgBa₂CuO₄ may be used.Materials useful for the substrate include sapphire or SrTiO₃ (strontiumtitanate). The substrate can be bi-crystal, thus facilitating theformation of a grain boundary upon deposition of a superconductinglayer, or the substrate can be formed using bi-epitaxial fabricationmethods. Methods for forming bi-epitaxial grain boundary junctions arewell known and described in the art. See, e.g., S. Nicolleti, H.Moriceau, J. Villegier, D. Chateigner, B. Bourgeaux, C. Cabanel, and J.Laval, “Bi-epitaxial YBCO grain boundary Josephson junctions on SrTiO₃and sapphire substrates”, Physica C, 269, 255 (1996), and the referencestherein, which is herein incorporated by reference in its entirety.

[0104] One implementation of a flux qubit involves a micrometer-sizedloop with three (or four) Josephson junctions. See J. E. Mooij, T. P.Orlando, L. Levitov, L. Tian, C. H. van der Wal, and S. Lloyd,“Josephson Persistent-Current Qubit,” Science 285, 1036 (1999) andreferences therein, which is herein incorporated by reference in itsentirety. The energy levels of this system correspond to differingamounts of magnetic flux threading the loop. Application of a staticmagnetic field normal to the loop may bring two of these energy levels(or basis states) into degeneracy. Typically, external ACelectromagnetic fields are also applied, to enable tunneling betweennon-degenerate states.

[0105] A radio-frequency superconducting quantum-interference device(rf-SQUID) qubit is another type of phase qubit having a state that canbe read by inductively coupling the rf-SQUID to rapidsingle-flux-quantum (RSFQ) circuitry. See R. C. Rey-de-Castro, M. F.Bocko, A. M. Herr, C. A. Mancini, and M. J. Feldman, “Design of an RSFQControl Circuit to Observe MQC on an rf-SQUID,” IEEE Trans. Appl.Supercond. 1, 1014 (2001) and references therein, which is herebyincorporated by reference in its entirety. A timer controls the readoutcircuitry and triggers the entire process with a single input pulse,producing an output pulse only for one of the two possible final qubitstates. The risk of this readout method lies in the inductive couplingwith the environment causing decoherence or disturbance of the qubitstate during quantum evolution. The circuitry attempts to reducedecoherence by isolating the qubit with intermediate inductive loops.Although this may be effective, the overhead is large, and the methodbecomes clumsy for large numbers of qubits.

[0106] In both above systems, an additional problem is the use of basisstates that are not naturally degenerate. Accordingly, the strength ofthe biasing field for each qubit has to be precisely controlled toachieve the desired tunneling between its basis states. This is possiblefor one qubit, but becomes extremely difficult with several qubits. Thefinger-SQUID phase qubit such as that shown in FIG. 2, providesnaturally degenerate basis states for quantum computation, and thuscombines benefits of existing qubit designs.

[0107] A permanent readout superconducting qubit (PRSQ) design was firstdisclosed by Alexandre Zagoskin, U.S. patent application Ser. No.09/452,749, “Permanent Readout Superconducting Qubit”, filed Dec. 1,1999, which is herein included by reference in its entirety. Anembodiment of a PRSQ 15 is shown in FIG. 1. PRSQ 15 can include a bulksuperconductor 10, a grain boundary 11, and a mesoscopic island 20(i.e., an island that has a size such that a single excess Cooper pairis measurable). PRSQ 15 can also include a switch 91, which may beconnected to a ground 92. Switch 91 can be a coherent superconductingswitch such as a superconducting SET or a parity key. The materialutilized in fabricating PRSQ 15 can be a high-T_(c) superconductorhaving a pairing symmetry that contains a dominant component withnon-zero angular moment, and a sub-dominant component that can have anypairing symmetry. The resulting qubit has the basis states ±ΔΦ withrespect to the phase, Φ, of the bulk superconductor. Another advantageof the PRSQ device is the highly localized phase states at the Josephsonjunction separating the mesoscopic island from the bulk. Although thePRSQ provides a robust system for quantum computation, realization offundamental quantum gate operations requires direct interaction with thephase of the device. Direct interaction with the state of the qubit canresult in decohering processes that require more sophisticatedtechniques for protecting the state of the qubit.

[0108] In accordance with the present invention, a finger-SQUID phasequbit device provides highly localized and naturally degenerate qubitbasis states, and a system for applying fundamental quantum computingoperations without a necessity for direct interaction with the state ofthe qubit device.

[0109]FIG. 2 illustrates an embodiment of the finger-SQUID phase qubitdevice according to the present invention. A qubit device 100 includes asuperconducting loop 360. Superconducting loop 360 has branches 130-1and 130-2. Device 100 further includes a superconducting finger 112,which includes a superconducting island 110. Leads 105-1 and 105-2 cancouple qubit device 100 to external circuitry that controls qubit device100. FIG. 2 illustrates a grain boundary 115 crossing branches 130-1 and130-2 and finger 112 of device 100. Junctions 120-1 and 120-2, which areformed where grain boundary 115 crosses branches 130-1 and 130-2,respectively, can control the behaviour of the device 100, whilejunction 111, which is formed where grain boundary 115 crosses finger112, can be formed to control operation parameters of a qubit 113 suchas the tunneling amplitude.

[0110] The change in phase of the order parameter across Josephsonjunction 111 in finger 112 forms the basis states for information inqubit device 100. If the order parameter has a phase of Φ where finger112 extends from loop 360, the order parameter has a change in phase of±ΔΦ across Josephson junction 111, depending on the direction ofcirculation of the ground state supercurrent. Therefore, the region ofqubit device 100 including finger 112 and the region where finger 112extends from loop 360 can then be referred to as qubit 113.

[0111] Finger 112 (including island 110) of device 100 can be asymmetricwith respect to branches 130-1 and 130-2 of loop 360 of device 100, asshown in FIG. 2. By forming finger 112 asymmetrically with respect tobranches 130-1 and 130-2 of loop 360, coupling between the flux in loop360 and finger 112 can be minimized. In some embodiments of theinvention, finger 112 can be symmetric with respect to branches 130-1and 130-2 and leads 105-1 and 105-2 of device 100. The position offinger 112 in device 100 with respect to leads 105-1 and 105-2 andbranches 130-1 and 130-2 will vary the effect of current through leads105-1 and 105-2 on superconducting island 110, and correspondingly, onthe ground state phase of qubit 113.

[0112] The angle of crystal orientation of superconducting material isrelated to the orientation of the superconducting order parameter. InFIG. 2, superconducting order parameter 101-1 is related to the angle ofcrystal orientation of device 100 on the side of grain boundary 115towards lead 105-1. Similarly, superconducting order parameter 101-2 isrelated to the angle of crystal orientation of device 100 on the side ofgrain boundary 115 towards lead 105-2. The angle of mismatch between thesuperconductor crystal lattice orientation on either side of grainboundary 115 can vary with respect to the orientation of grain boundary115 for different embodiments of the invention. When junction 111 is agrain boundary Josephson junction, the angle of misorientation of thesuperconductor crystal lattice above and below grain boundary 115 candetermine the ground state of qubit 113. The angle of orientation can bechosen to control the operation of the qubit device 100. Note that inthis context, the term “superconductor crystal lattice” refers to thecrystal lattice of the material that comprises parts of qubit device 100(e.g. superconducting loop 360 and superconducting finger 112) and issuperconducting during device operation. However, it is notsuperconducting under all conditions (e.g. it will be in the normalstate if the temperature, magnetic field, or current is too high).Further, the superconducting order parameter may be suppressed inJosephson junctions 120-1, 120-2, and 111 of qubit device 100.

[0113] In some embodiments of the invention, superconducting orderparameter 101-1 is misoriented with respect to superconducting orderparameter 101-2. For example, superconducting order parameter 101-1 canbe oriented at an angle of about 45 degrees with respect to theorientation of superconducting order parameter 101-2. Other embodimentsmay use other non-zero misorientations.

[0114] Further, for at least one of the Josephson junctions 120-1,120-2, and 111 of qubit device 100, the superconductor crystal latticemay have about a 45° misorientation angle with respect to theorientation of grain boundary 115, such that a ground state π/2 phaseshift is induced in transition across the Josephson junction.

[0115]FIG. 2 illustrates some dimensions of an embodiment of theinvention. In this embodiment, the width of island 110, W₁₁₀, can rangebetween roughly 0.1 μm and roughly 0.5 μm and the length of the islandL₁₁₀ can range between roughly 0.5 μm and roughly 1 μm. The portion offinger 112 not including island 110 can have a length L₁₁₂ less thanroughly 2 μm. Superconducting loop 360 can have a width W₁₃₁ rangingbetween roughly 0.5 μm and roughly 5 μm. The length of the region ofloop 360 that finger 112 extends from, L₁₃₂, can range between roughly0.5 μm and roughly 2 μm, and the length of the opposite region in thesuperconducting loop, L₁₃₃, can have the same range. In some embodimentsof the invention, the lengths L₁₃₂ and L₁₃₃ can be different. The widthof branch 130-1, W₁₃₀₋₁, can range between roughly 0.2 μm and roughly 2μm, and the width of branch 130-2, W₁₃₀₋₂, can have a similar range. Insome embodiments of the invention, widths W₁₃₀₋₁ and W₁₃₀₋₂ can bedifferent. In an embodiment of the invention, Josephson junction 111 ofFIG. 2 can have a capacitance C of about 10⁻¹⁴ F, and a correspondingCoulomb energy E_(c) of about 20 GHz. Junction 111 can have a criticalcurrent I_(c) of about 100 nA, and a corresponding Josephson energyE_(J) of about 300 GHz. The plasma frequency ω_(P) can be about 25 GHz,and the phase difference across junction 111, ΔΦ, can be about 0.2π.

[0116]FIGS. 3A to 3D illustrate an embodiment of a method forfabricating a finger-SQUID qubit device. For example, substrate 50 ofFIG. 3A can be a bi-crystal substrate or a bi-epitaxial substrate. Firstregion 51 of substrate 50 has a first crystal lattice orientation, whilesecond region 52 of substrate 50 has a second crystal latticeorientation. Superconducting material 55 is deposited on substrate 50,as shown in FIG. 3B. The crystal lattice orientation of superconductingmaterial 55 aligns with the crystal lattice orientation of theunderlying substrate 50. Therefore, superconducting material 55deposited on first region 51 of substrate 50 has a crystal latticeorientation aligned with the first crystal lattice orientation, whilesuperconducting material 55 deposited on second region 52 of substrate50 has a crystal lattice orientation aligned with the second crystallattice orientation. As a result, grain boundary 115 can be formedbetween the regions of superconducting material 55 having differentcrystal lattice orientations.

[0117] Superconducting material 55 can be patterned according towell-known methods, as shown in FIG. 3C (side view) and FIG. 3D (topview). The formation and behaviour of grain boundary Josephson junctionsis well known and described in the art. See, e.g., E. Il'ichev, M.Grajcar, R. Hlubina, R. Ijsselsteijn, H. Hoenig, H. Meyer, A. Golubov,M. Amin, A. Zagoskin, A. Omelyanchouk, and M. Kupriyanov, “DegenerateGround State in a Mesoscopic YBa₂Cu₃O_(7−x) Grain Boundary JosephsonJunction”, Phys. Rev. Letters, 86, 5369 (June 2001), and the referencestherein, each of which is incorporated by reference in its entirety.

[0118] Referring again to FIG. 2, the ground state phase differenceacross junctions 120-1 and 120-2 can depend on the orientation of thebranch with respect to the grain boundary. Thus the junctions 120-1 and120-2 can have a ground state phase difference chosen to tuneinteraction of the device with the surrounding environment. The orderparameters 101-1 and 101-2 are related to the crystal latticeorientations of the superconductor and the underlying substrate. Inorder to form a grain boundary junction, where order parameters 101-1and 101-2 are suppressed at the grain boundary, a bi-crystal substrateor a bi-epitaxial substrate may be used. Methods for fabricating grainboundary junctions using bi-crystal fabrication methods and bi-epitaxialfabrication methods are well known.

[0119] An embodiment of the invention can include a bi-epitaxialsubstrate, and an array of finger SQUID qubit devices, fabricated sothat the superconducting loop and the superconducting finger cross thegrain boundary of the substrate. The finger SQUID qubit devices arepatterned using a superconducting material that violates time reversalsymmetry. Materials that are useful as a substrate include sapphire orstrontium titanate, for example. The devices can be patterned using anunconventional superconductor material such as a d-wave superconductor.An example of a d-wave superconductor is YBa₂Cu₃O_(7−x), where x isbetween 0 and 0.6. Additional examples includeBi₂Sr₂Ca_(n−1)Cu_(n)CO_(2n+4), Tl₂Ba₂CuO_(6+x), and HgBa₂CuO₄. The angleof misorientation of the superconductor crystal lattice with respect tothe grain boundary can be chosen to optimize the characteristics of thedevice. The superconductor crystal lattice orientation can have a 0°-45°change with respect to the orientation of the grain boundary. That is,the superconductor crystal lattice on one side of the grain boundary maybe aligned with the direction of the grain boundary, while thesuperconductor crystal lattice on the other side of the grain boundarymay be aligned at about a 45° angle with the direction of the grainboundary.

[0120]FIG. 4 illustrates an embodiment of the invention wherein theground state phase difference across Josephson junctions 120-1 and 120-2can be controlled. As FIG. 4 shows, the orientation of grain boundary115 may change across device 100. Changing the angle of misorientationacross the grain boundary can modify the critical current of junction111, thus providing control over the tunneling amplitude of qubit 113.

[0121] Grain boundary 115 is formed by forming a misorientation in thecrystal lattice of the superconducting material. That is, the crystallattice of the superconducting material on the side of grain boundary115 towards lead 105-1 is misoriented with respect to the crystallattice of the superconducting material on the opposite side of grainboundary 115. Order parameter 101-1 and order parameter 101-2, whichcorrelate with the crystal lattice orientation of the superconductor,take on angles A₁₀₁₋₁ and A₁₀₁₋₂ respectively. The angle ofmisorientation across the grain boundary A₁₀₁₋₁-A₁₀₁₋₂ correlates withphase difference of the grain boundary Josephson junction. Angles A₁₂₀₋₁and A₁₂₀₋₂ can be varied to further control the phase difference ofJosephson junctions 120-1 and 120-2. Angles A₁₂₀₋₁ and A₁₂₀₋₂ are chosento optimize the operational parameters of superconducting loop 360 ofdevice 100. An embodiment of the invention can make use of anglesA₁₀₁₋₁, A₁₀₁₋₂, A₁₂₀₋₁, and A₁₂₀₋₂ to control the phase differenceacross junctions 120-1 and 120-2, respectively, and consequently thedevice control over the qubit characteristics.

[0122] The phase difference across junctions 120-1, 120-2, and 111 maybe different for each junction or may be the same for some or all of thejunctions. For example, in a particular embodiment of the invention, thesuperconductor crystal lattice has a 0°-45° misorientation with respectto grain boundary 115. That is, the superconductor crystal lattice onone side of grain boundary 115 may be aligned with the direction of thegrain boundary, while the superconductor crystal lattice on the otherside of grain boundary 115 may be aligned at about a 45° angle with thedirection of the grain boundary. Josephson junctions 120-1 and 120-2 canhave different orientation angles A₁₂₀₋₁ and A₁₂₀₋₂. For example,junction 120-1 can have an angle A₁₂₀₋₁ of 0°, and junction 120-2 canhave an angle A₁₂₀₋₂ of about 22.5°. In this embodiment, junctions 120-1and 111 are π/2-phase shift Josephson junctions, while junction 120-2 isa 0-phase shift Josephson junction. In another embodiment of theinvention, junctions 120-1 and 120-2 can have angles A₁₂₀₋₁=A₁₂₀₋₂=0°respectively.

[0123] Behaviour of symmetric and asymmetric SQUIDS has been describedin U.S. patent application Ser. No. 09/823,895, M. Amin, T. Duty, A.Omelyanchouk, G. Rose, A. Zagoskin, and J. Hilton, “High Sensitivity,Directional DC-SQUID Magnetometer”, filed Mar. 31, 2001, and hereinincorporated by reference in its entirety; and I. Borisenko, P. Mozhaev,G. Ovsyannikov, and K. Constantinian, “Superconducting Current-PhaseDependence in High-T_(c) Symmetrical Bicrystal Junctions”, SQUID 2001conference proceedings (Sep. 2, 2001), and the references therein,herein incorporated by reference in its entirety.

[0124] Referring again to FIG. 4, superconducting island 110 should bemesoscopic in size, such that it is sensitive to the presence or absenceof a single Cooper pair. The capacitance of superconducting island 110is related to the width of the Josephson junction 111; therefore, thetunneling amplitude of qubit 113 depends in part on the width of island110. Modifying the angle of branches 130-1 and 130-2, or the angle ofthe grain boundary (as illustrated by angles A₁₂₀₋₁ and A₁₂₀₋₂), canchange the ground state phase difference across junctions 120-1 and120-2 respectively. Thus, the crystal lattice misorientation angleshould be chosen to optimize the operational parameters of the island110 of the device.

[0125]FIG. 5 illustrates an embodiment of a quantum register 300.Quantum register 300 includes an array of N finger SQUID qubit devices100-1 through 100-N. The illustrated substrate region 350 can be abi-epitaxial substrate such that the orientation of the crystal latticecan change across grain boundary 115. The orientation of the orderparameters 101-1 and 101-2 of the superconducting material are relatedto the crystal lattice orientation of the substrate. The superconductingmaterial can have an angle of misorientation in the order parameter,with respect to the grain boundary, such that the operational parametersof the device can be optimized.

[0126] In order to perform quantum computation, a quantum register suchas quantum register 300 in FIG. 5 provides a universal set of basicquantum operations, such that any quantum gate can be implemented. Insome cases, the universal set can include a {circumflex over (σ)}_(x) ortunnel matrix operation, a {circumflex over (σ)}_(z) or bias operation,and an entanglement operation. In quantum register 300, the {circumflexover (σ)}_(x) matrix is correlated the tunneling amplitude of the qubitfor each qubit device 100-1 through 100-N. The operators {circumflexover (σ)}_(x) and {circumflex over (σ)}_(z) are the well known Paulimatrices, which for a doubly degenerate system can be represented asshown in Equations 1 and 2. $\begin{matrix}{{\hat{\sigma}}_{x} = \begin{pmatrix}0 & 1 \\1 & 0\end{pmatrix}} & {{Equation}\quad 1} \\{{\hat{\sigma}}_{z} = \begin{pmatrix}1 & 0 \\0 & {- 1}\end{pmatrix}} & {{Equation}\quad 2}\end{matrix}$

[0127] Control of the tunneling matrix operation or {circumflex over(σ)}_(x) is not necessary as long as the tunneling is effectivelysuppressed while the other operations are applied. For example, theother operations can be controlled with a time constant τ_(c), such thatτ_(c)≦Δ⁻¹, where Δ is the tunneling amplitude of the qubit. Furthermore,if the other quantum gates require a time τ_(c)≧Δ⁻¹, refocusingtechniques can be applied to maintain the correct state in the quantumregister. Refocusing techniques are well known in the art and describedin D. Lidar, and L. Wu, “Reducing Constraints on Quantum Computer Designby Encoding Selective Recoupling,” LANL quant-ph/0109021, September,2001, which is herein incorporated in its entirety. The entanglementoperation needs to entangle the quantum states of selected qubits in thequantum register in order to implement many crucial quantum algorithms.See, e.g., U.S. Pat. No. 5,768,297, Peter Shor, “Method for reducingdecoherence in quantum computer memory”, filed October 1996, and thereferences therein, each of which is hereby incorporated by reference inits entirety. In an embodiment of the invention, an entanglementoperation can be a controlled phase shift CP. Controlled phase shiftoperations are well known and described by the Pauli matrix of equation3. $\begin{matrix}{{CP} = \begin{pmatrix}1 & 0 & 0 & 0 \\0 & {- 1} & 0 & 0 \\0 & 0 & {- 1} & 0 \\0 & 0 & 0 & 1\end{pmatrix}} & {{Equation}\quad 3}\end{matrix}$

[0128] Referring to FIG. 6, an embodiment of the invention includes amechanism for coupling qubits 113-N−1 and 113-N in a quantum register300 of M finger SQUID qubit devices 100-1 through 100-M. Finger SQUIDqubit devices 100-N−1 and 100-N in quantum register 300 can be coupledto perform an entanglement operation; that is, when the wavefunctions ofthe respective qubits are allowed to overlap. A mechanism for providingan entanglement operation between qubits includes a coherent,superconducting coupling link 315-N−1,N between the superconductingislands 110-N−1 and 110-N. The superconducting coupling link 315-N−1, Nof this embodiment provides a mechanism for supercurrent to flowcoherently between qubits 113-N−1 and 113-N of qubit devices 100-N−1 and100-N, thus entangling the states of the qubits. The superconductingcoupling link can further provide a coupling switch 895 to open or closethe coupling link between the qubits. Coupling switch 895 may be acoherent supercurrent switch such as a parity key or coherent SET(single electron transistor) device.

[0129]FIG. 6 illustrates a quantum register 300 formed from an array offinger SQUID qubit devices 100-1 through 100-M, wherein a mechanism forentangling the state of qubits is illustrated. Superconducting link315-N−1,N provides a coherent connection between qubit devices 100-N−1and 100-N when coupling switch 895 is closed. Interface junctions316-N−1 and 316-N provide coherent connections between qubit devices100-N−1 and 100-N respectively. Junctions useful for forming theinterface junctions 316-N−1 and 316-N include coherent heterostructurejunctions. Coherent heterostructure junctions provide a coherenttransition between an unconventional superconducting material and aconventional superconducting material.

[0130] A method for fabricating superconducting link 315-N−1,N andheterostructure junctions 316-N−1 and 316-N includes depositing aninsulating material over an array of finger SQUID qubit devices, etchingand developing regions of the insulating material to expose theunderlying superconducting islands 110-N−1 and 100-N, depositing aconductive material over the entire chip, etching and developing theconductive material such that it remains only in the exposedsuperconductor areas, depositing a superconducting material over theentire chip, and etching and developing the superconductor material topattern connections between the underlying exposed qubit devices. Theresult of such a fabrication process is an array of coupled qubits, allof which are coupled through heterostructure junctions such as junction316-N and 316-N−1. Furthermore, heterostructure junctions 316-N and316-N−1 provide a means for coupling two different types ofsuperconductor together. Superconducting link 315-N−1, N can be aconventional superconducting material such as niobium (Nb), aluminum(Al), or lead (Pb). Methods for fabricating coherent SET devices orparity keys using conventional superconductors such as Nb or Al are wellknown in the art. Heterostructure junctions such as heterostructurejunctions 316-N and 316-N−1 and their preparation are described inpreviously filed patent application, attorney reference number M-12300,filed on Dec. 6, 2001, entitled “Trilayer Heterostructure Junctions,” byAlexanderTzalenchuk, Zdravko Ivanov, and Miles F. H. Steininger, whichis hereby incorporated by reference in its entirety.

[0131] A method of controlling superconducting link 315-N−1,N isprovided, such that the states of qubit 113-N−1 and qubit 113-N can beentangled when required. Superconducting link 315-N−1,N includes a firstlead 315-N−1, A and a second lead 315-N, B as shown in FIG. 6.Controllable entanglement can be accomplished by introducing a coherentcoupling switch 895 in the superconducting link 315-N−1,N such that whenthe switch is closed, superconducting link 315-N−1,N coherently conductssupercurrent, and when the switch is open, superconducting link315-N−1,N does not conduct. A mechanism for controllably coupling aqubit 113-N and qubit 113-N−1 includes providing first lead 315-N−1,Afrom qubit 113-N−1 to coupling switch 895, and providing second lead315-N,B from qubit 113-N to coupling switch 895. In operation, withcoupling switch 895 in the open state, qubits 113-N and 113-N−1 will bede-coupled, whereas, with coupling switch 895 in the closed state,qubits 113-N and 113-N−1 will be coupled.

[0132] Coupling switch 895 in FIG. 6 illustrates a superconducting SETdevice 895. Island 81 is isolated by tunnel junctions 83-1 and 83-2, anda voltage can be capacitively coupled to island 81 using electrode 82.One side of SET 895 connects to first lead 315-N−1,A, while the otherside connects to the second lead 315-N-B. The voltage coupled to island81 using electrode 82 provides a means to tune superconducting island 81of coupling switch 895, for example the SET device shown here, to allowpassage of single electrons or pairs of electrons between the leads315-N−1,A and 315-N-B.

[0133] Island 81 of SET device 895 can have a width corresponding to thewidth of tunnel junctions 83-1 and 83-2, and a length on the order ofabout 5 μm or less. The length of island 81 can be on the order of about2 μm or less, or in some embodiments the length of island 81 can be onthe order of about 0.5 μm. Electrode 82 can be formed on the order ofabout 0.5 μm from the superconducting island 81. Tunnel junctions 83-1and 83-2 that separate superconducting island 81 of the device fromleads 315-N−1,A and 315-N,B can include a non-superconducting layerbetween the island 81 and the and the respective lead. Tunnel junctions83-1 and 83-2 can have small capacitances such that the Josephson energyof the junctions is much less than the Coulomb energy of the device.

[0134] Charging electrode 82 can change the ratio of the Coulomb energyto the Josephson energy in the device, thus controlling the flow ofcurrent across island 81. The material forming the intermediate layer oftunnel junctions 83-1 and 83-2 can have a dielectric value such that theJosephson energy of the junctions is much less than the Coulomb energyof the device. The thickness of the intermediate layer of tunneljunctions 83-1 and 83-2 is chosen in a regime such that the Josephsonenergy of the junctions are much less than the Coulomb energy of thedevice, but not so large as to reduce tunneling effects. Some materialsthat are useful for forming the intermediate layer of the junctions arealuminum oxide (Al₂O₃), or a normal metal such as gold. Preparation oftunnel junctions 83-1 and 83-2 and island 81 can include use ofelectron-beam lithography, and shadow mask evaporation techniques.Methods for forming tunnel junctions such as tunnel junctions 83-1 and83-2 are well known as described in the art. The area of the junctionscan be on the order of about 0.5 μm² or less. In some embodiments of theinvention, the area of said tunnel junctions can be on the order ofabout 0.1 μm or less, and in other embodiments the area of said tunneljunctions can be on the order of about 60 nm² or less. The behavior ofSETs is well defined and is discussed in detail in P Joyez et al.,“Observation of Parity-Induced Suppression of Josephson Tunneling in theSuperconducting Single Electron Transistor,” Physical Review Letters,Vol. 72, No. 15, Apr. 11, 1994, herein incorporated by reference in itsentirety, and D. Born, T. Wagner, W. Krech, U. Hubner, and L. Fritzch,“Fabrication of Ultrasmall Tunnel Junctions by Electron BeamDirect-Writing”, IEEE Trans. App. Superconductivity, 11, 373 (March2001), and the references therein, which is herein incorporated in itsentirety.

[0135] Another mechanism for providing entanglement between qubitsincludes a superconducting loop between qubit devices 100-N−1 and 100-N.This superconducting loop can have a switch, such that when the switchis open, the superconducting loop cannot inductively couple to thequbits, and when the switch is closed the superconducting loop doesinductively couple to the qubits, thus providing a mechanism forcontrollably entangling the states of the qubits.

[0136]FIG. 7 shows another mechanism for providing entanglement betweenqubits, which includes providing a direct, coherent link between therespective qubit devices to be coupled, and providing an electrode,wherein the electrode is capacitively coupled to the coherent link. Theelectrode can provide a mechanism for controlling the charging energy ofthe coherent link, such that the link permits the flow of supercurrentor prevents the flow of supercurrent.

[0137]FIG. 7 illustrates a region of a quantum register 300 inaccordance with an embodiment of the invention. Switch 895 maycoherently couple qubit devices 100-N−1 and 100-N. Switch 895 caninclude electrode 82 for controlling the charging state of link315-N−1,N between qubit device 100-N−1 and 100-N. Alternately, switch895 can include a superconducting SET or parity key, for coherentlycoupling the respective qubit devices. FIG. 7 illustrates a parity keythat includes two tunnel junctions, 316-N−1 and 316-N, link 315-N−1,N,and electrode 82, wherein electrode 82 is capacitively coupled to link315-N−1,N.

[0138]FIG. 8 illustrates a mechanism for providing a biasing operationor {circumflex over (σ)}_(z) or bias gate can be introduced the fingerSQUID qubit device 100-N−1 by providing a coherent, superconducting link317-N−1 between superconducting island 110-N−1 and a region ofsuperconducting loop 360-N−1. FIG. 8 illustrates this connection,wherein a coherent, controllable superconducting link 317-N−1 isprovided between superconducting island 110-N−1 and superconducting loop360-N−1. Link 317-N−1 can be controlled by coherent switching mechanism898-N−1, where coherent switching mechanism 898-N−1 may include asuperconducting SET as described above for the qubit-qubit controllablecoupling mechanism 895.

[0139] Some embodiments of the invention can include a plurality ofsuperconducting fingers extending to the interior of a singlesuperconducting loop. Since the quantum information is stored at theJosephson junction in the finger, the superconducting loop becomes aquantum register 601-N for controlling a plurality of qubits. FIG. 9illustrates a quantum register 600, which includes quantum register601-N in accordance with an embodiment of the invention. Quantumregister 601-N includes a superconducting loop 360-N, wherein Lsuperconducting fingers and L corresponding superconducting mesoscopicislands 110-N,1 through 110-N,L can be formed. Quantum register 600 canalso include one or more of quantum registers 601. Passing currentacross the leads of superconducting loop 360-N, such that the current isgreater than the critical current of Josephson junctions 120-1-N and120-2-N respectively, can have the effect of collapsing the wavefunctionof one or more of the qubits 113-N,1 through 113-N,L in quantum register601-N, thus providing the basis for readout and initializationoperations. Further, qubits in quantum register 601-N may be entangledby coupling any of the qubits 113-N,1 through 113-N,L. For example,qubits 113-N,1 through 113-N,L may be coupled by providing acontrollable coupling mechanism 895 as described above with regard toFIG. 8.

[0140] Furthermore, in some embodiments, bias operations, readout andinitialization can be performed on each qubit 113-N,1 through 113-N,Lseparately. To perform a bias operation, readout, or initialization onqubit 113-N,1, a controllable, coherent superconducting link similar tolink 317-N of FIG. 8 can be provided between superconducting island110-N,1 and superconducting loop 360-N.

[0141] A method for biasing the state of a qubit in quantum register601-N of FIG. 9, wherein a controllable, coherent superconducting linkis provided between the island 110-N,1 and superconducting loop 360-N,includes closing switch 898-N,1 such that island 110-N,1 is coherentlycoupled to loop 360-N.

[0142] A method for initializing the state of qubit 113-N,1 includesclosing switch 898-N,1 such that island 110-N,1 is coherently coupled tosuperconducting loop 360-N, and driving a bias current across the leadsof superconducting loop 360-N. The direction of the bias current passingthrough superconducting finger 112-N,1 correlates with one of the basisstates of qubit 113-N,1. For example, passing a bias current throughfinger 112-N,1 in a first direction can initialize qubit 113-N,1 to afirst basis state, and passing a bias current through finger 112-N,1 ina second direction can initialize qubit 113-N,1 to a second basis state.This operation will select a state in qubit 113-N,1 that correspondswith the direction of the bias current. In some embodiments, the biascurrent can exceed the critical current of the junction. Although FIG. 9does not show a switch for each qubit 113-N,1 through 113-N,L, a switchmay be provided for each qubit in quantum register 601-N.

[0143] A method for reading out the state of a qubit in quantum register601-N includes closing switch 898-N,1 such that island 110-N,1 iscoherently coupled to superconducting loop 360-N, passing a bias currentacross the leads 105-1 and 105-2, and measuring the potential changeacross the leads. Driving a bias current through superconducting finger112-N,1 has the effect of biasing one of the qubit basis states. If thebias current exceeds the critical current of the Josephson junction onfinger 112-N,1, then the junction enters the dynamical regime and avoltage results. When the bias current is driven through finger 112-N,1,qubit 113-N,1 will first collapse to one of its basis states. This firstcollapse is based on the quantum state of qubit 113-N,1 and not thedirection of the bias current. In a first case, the collapsed state ofqubit 113-N,1 correlates with the direction of the bias current, thusresulting in a first characteristic voltage behaviour at the junction.In a second case, the collapsed state of qubit 113-N,1 will correlatewith an opposing bias current, thus resulting in a second characteristicvoltage behaviour. Thus, measuring the potential change across leads105-1 and 105-2 provides a measurement of the characteristic voltageresulting from the bias current. By correlating the resultingcharacteristic voltage with the basis states of qubit 113-N,1, a readoutoperation can be performed. In all of the above cases the duration ofthe current pulse depends on the embodiment of the invention. Theduration of the current pulse can be on the order of the tunnelingamplitude of qubit 113-N,1. The current pulse can have a duration τranging as Δ_(min)≦1/τ≦5Δ_(max), where Δ_(min) is the smallest tunnelingamplitude in quantum register 601-N, and Amax is the largest tunnelingamplitude in quantum register 601-N. Furthermore, the magnitude of thebias current depends upon the embodiment of the invention. The biascurrent can have a magnitude ranging between 0≦|I_(B)|≦5I_(c) ^(max),where I_(c) ^(max) is the largest critical current of thesuperconducting finger junction in quantum register 601-N. In someembodiments of the invention the bias current can range between 0 and2I_(c) ^(max).

[0144] In order that a qubit device be useful as a quantum register, amechanism to readout and initialize the state of the qubit is provided.The finger SQUID qubit device provides a robust system for providingreadout and initialization operations. When the qubit is decoupled fromits surroundings, it evolves quantum mechanically as a superposition ofits basis states. Referring to FIG. 10, if superconducting island 110 isgrounded, qubit 113 becomes coupled to its surroundings and thewavefunction collapses, leaving qubit 113 restricted to one of its basisstates. Island 110 can be grounded, for example, by closing switch 891.While grounded, qubit 113 cannot evolve quantum mechanically and is saidto hold classical information because it occupies one of its groundstates (basis states) which can be treated as the bitstates 0 and 1.

[0145] A method for performing a quantum computation using an embodimentof the invention includes initializing each of the qubits in a quantumregister (to one basis state), evolving the qubits in the quantumregister according to the applied quantum algorithm, wherein evolvingthe qubit includes application of the quantum operations provided by theembodiment of the invention, grounding the qubits in the quantumregister to collapse the wavefunction of the respective qubits, andreading out the state of each of the qubits in the quantum register. Insome embodiments, a separate grounding operation is not performed. Aseparate grounding operation is not required since the qubits collapseinto a basis state upon a measurement of the qubit state, including whenexecuting a readout operation. In some methods for performing quantumcomputation, readout of the state of the qubit can be performedthroughout the calculation. See e.g., P. Shor, U.S. Pat. No. 5,768,297,referenced above.

[0146] A mechanism for grounding the qubit includes a mechanism fordecohering the wavefunction of the qubit. Referring again to FIG. 10, anembodiment of the current invention can include a grounding mechanismwherein superconducting island 110 is connected to ground 892. Since thebasis states of qubit 113 are characterized by a phase change ±ΔΦ acrossjunction 111 with respect to the phase Φ of the superconducting orderparameter in the region of the device from which finger 112 extends,grounding island 110 can fix the phase of qubit 113 to either the |+ΔΦ>or |−ΔΦ> state. Ground 892 can be a bulk superconductor having a fixedphase. A superconducting link between superconducting island 110 andground 892 can include a grounding switch 891, for coupling anddecoupling qubit 113 to ground 892. Grounding switch 891 can be a SETdevice or a parity key. When grounding switch 892 is closed, qubit 113is fixed to a single basis state, and when grounding switch 891 is open,qubit 113 decouples from its surroundings and can evolve quantummechanically as a superposition of its basis states.

[0147]FIG. 10 illustrates a grounding switch 891 and ground 892.Superconducting island 110 is connected directly to grounding switch 891such that if the switch is open island 110 can be decoupled from ground892 and if the switch is closed island 110 can be coupled to ground 892.When island 110 is coupled to ground 892, qubit 113 will remain fixed toone of its basis states. The grounding system has been described indetail in U.S. patent application Ser. No. 09/872,495, M. Amin, G. Rose,A. Zagoskin, and J. Hilton, “Quantum Processing System for aSuperconducting Phase Qubit”, filed Jun. 1, 2001, and the referencestherein, herein incorporated by reference in its entirety.

[0148] Another mechanism for grounding a finger SQUID qubit deviceincludes driving a current across the leads of the device. Referringagain to FIG. 10, in operation, if no current is driven across deviceleads 105-1 and 105-2, superconducting island 110 may be decoupled fromits surroundings and thus the state of the qubit can evolve quantummechanically. When a current is driven across the leads of the devicethe superconducting loop couples to superconducting island 110 and thequbit wavefunction collapses into one of its basis states.

[0149] In another embodiment of the invention, a bias operation can beperformed by driving a current across leads 105-1 and 105-2 of FIG. 10,such that the current is less than the critical current of Josephsonjunctions 120-1 and 120-2. If the current is less than the criticalcurrent of junctions 120-1 and 120-2, the quantum state of the qubitwill not collapse. The sign of the current across leads 105-1 and 105-2can be chosen to select the state to be biased. For example, driving acurrent with a magnitude I, from lead 105-1 to lead 105-2 can bias thequantum state of the qubit 113 towards a first state, and driving acurrent with a same magnitude I, from lead 105-2 to 105-1 can bias thequantum state of the qubit 113 to a second state. Thus, although acontrollable coherent link between the superconducting island 110 andsuperconducting loop 360 may be used to initialize and readout thequbit, such a link is not necessary.

[0150] In accordance with an embodiment of the invention, finger SQUIDqubit device 100 can be placed in a control system 800 providing amechanism for driving a bias current across leads 105-1 and 105-2 ofFIG. 10, and a mechanism for measuring a potential change across leads105-1 and 105-2. Furthermore, control system 800 can include a mechanismfor controllably coupling superconducting island 110 to superconductingloop 360, or a mechanism for controllably coupling superconductingisland 110 to ground 892.

[0151] The control system illustrated in FIG. 10 provides a mechanism890 for driving a bias current across the leads of the qubit device, amechanism 896 for measuring the potential change across the leads of thedevice, and a grounding switch 891 for grounding the island 110 of thedevice to ground 892. Such a control system can provide all of theoperations required to perform quantum computation, such asinitialization, application of quantum gates, grounding, and readout ofthe qubit state. In some embodiments of the invention, the groundingswitch 891 can be left out of the control system, and grounding thequbit can include driving a current across the leads of the device.

[0152] After grounding, qubit 113 has collapsed to one of its basisstates. A mechanism for performing a readout operation on qubit 113includes a mechanism for reading out the basis state that qubit 113occupies. Thus, a mechanism for performing a readout operation on qubit113 can include grounding qubit 113, applying a current across the leadsof the device 105-1 and 105-2, and measuring the response of thecurrent. When a current is driven across the leads of the device 105-1and 105-2, a response can be measured that depends on which basis statequbit 113 occupies, as described previously. Another embodiment of amechanism for performing a readout operation on qubit 113 includesapplying a bias current between the leads 105-1 and 105-2, and measuringthe resulting potential change across the device.

[0153]FIG. 11 illustrates a plan view of a quantum processor 900including control system 800 wherein a readout operation for the stateof a finger SQUID qubit device can be performed. System 800 includesquantum register 300 of N finger SQUID qubit devices, current source890, voltage measuring device 896, coupling switches 895-1 to 895-N−1,current switches 894-1 to 894-N, branch switches 898-1 to 898-N, andisland grounding switches 891-1 to 891-N. The control system illustratedin FIG. 11 can ground and perform a readout operation on each of thequbits in register 300. A method for reading out the state of a registerof finger SQUID qubit devices includes closing the switch 894-1, drivinga current with the current source 890, and measuring a voltage with thevoltage measuring device 896. The process can then be repeated for eachqubit in the register.

[0154] Another method for reading out the state of a finger SQUID qubitdevice register includes closing a switch 891-1, such that therespective superconducting island 110-1 is grounded, then driving acurrent with current source 890, and measuring the potential change withvoltage measuring device 896, then repeating the process for each qubitin the register. The value measured by voltage measuring device 896 canbe correlated with the basis state of the qubit and that information canbe transferred to a binary memory device. For example, FIG. 11 furthershows a classical driver system 897 for controlling the operations inthe quantum register. Classical driver system 897 can provide aclassical memory for storing output from the quantum calculations.Furthermore, classical driver system 897 can store a set of operationsto run on the quantum register. Classical driver system 897 can, forexample, include a conventional microprocessor with memory to storeprograms and data.

[0155] A control system such as that illustrated in FIG. 11 provides amechanism for initialization of the qubit state. The state that eachqubit in the register is initialized to depends on the quantum algorithmto be calculated. In some embodiments, all the qubits in the quantumregister can be initialized to the basis state |1> (as stated above, the|0> state may arbitrarily be chosen as either of the two basis states|+ΔΦ> or |−ΔΦ>). Initialization of finger SQUID qubit 113-1 includesclosing current switch 894-1, and driving a current using a currentsource 890 for a duration τ. The duration τ can vary over a range asdescribed above for the quantum register operations. Driving a currentacross the leads of device 100-1 has the effect of biasing one of thebasis states of qubit 113-1. Once current switch 894-1 has been opened,qubit 113-1 will no longer be grounded, and it can begin to evolvequantum mechanically. By repeating the process, each of the qubits 113-1through 113-N may be initialized in series. Another method forinitializing the state of quantum register 300 can includesimultaneously initializing N qubits in the quantum register of system800 to the same basis state. A method for initializing N qubits in aquantum register of finger SQUID qubit devices in parallel can includeclosing current switches 894-1 through 894-N concurrently, and driving acurrent using current source 890. The current travels across the leadsof each of the qubit devices in the register, therein initializing thequbit to the basis state corresponding to the direction of the current.

[0156] An alternative embodiment of the control system 800 can includeonly one set of switches 894-1 to 894-N or 891-1 to 891-N. Since amechanism for grounding, readout, and initialization can be implementedusing only one set, a control system does not require both sets ofswitches. For example, in an embodiment of the control system 800,switches 891-1 through 891-N are not present. A mechanism forinitializing qubit 113-1 can include closing switch 891 and driving acurrent using the current source 890. Furthermore, a mechanism forreadout of the state of the quantum register can include closing switch894, driving a current using the current source 890, and measuring theresulting potential change using the voltage measuring device 896. Themeasured voltage can then be correlated with the respective basis stateof the qubit and then transferred to a memory register. The classicalmemory register may be included in classical driver system 897 of system800.

[0157] In some embodiments of the invention, a quantum register cancontain a multi-dimensional array of finger SQUID qubit devices. Forexample, FIG. 13 shows a two dimensional array of finger SQUID qubitdevices. The superconducting island 100 of each of the devices may beconnected to the superconducting islands of other qubit devices in thearray. Alternately, in accordance with another embodiment of theinvention, a control system can include a separate current source andvoltage measurement device for each qubit in quantum register 300. Forexample, FIG. 11 may be modified so that each qubit device 100-1 through100-N has a current source and a voltage measurement device. Thus eachqubit can be directed independently of other qubits, and the qubit-qubitcoupling can be accomplished as described previously. See, e.g.,commonly assigned patent application Ser. No. 09/872,495, “QuantumProcessing System and Method for a Superconducting Phase Qubit,”assigned to the same assignee as is the present disclosure, which ishereby incorporated by reference in its entirety.

[0158] In some embodiments, voltage measurement device 896 can be aradio-frequency single electron transistor (RF-SET), capable ofmeasuring a magnitude on the order of microvolts on a time-scale ofpicoseconds. See i.e., R. J. Schoelkopf, P. Wahlgren, A. A. Kozhevnikov,P. Delsing, D. E. Prober “The Radio-Frequency Single-Electron Transistor(RF-SET): A Fast and Ultrasensitive Electrometer”, Science, 280, 1238(May 1998), herein incorporated by reference in its entirety.

[0159] Referring to FIG. 12, RF-SET voltmeter 140 is comprised ofsuperconducting SET 709, tank circuit 712, and port 706 for applying anddetecting a signal. SET 709 can be made of any superconducting material,for example niobium, aluminum, lead, tin, or any high-temperaturesuperconducting cuprate. A RF-SET as described in R. Schoelkopf et al.,can include a SET placed in a high quality factor tank circuit tuned toresonance. Tank circuit 712 can include an inductor and a capacitor. Thecapacitor is coupled in parallel with SET 709. A third terminal of SET709 is coupled to an electrode. In operation, a radio-frequency ormicrowave signal is introduced into tank circuit 712. The reflectedsignal is a function of the conductance of SET 709. Analysis of thereflected signal using established techniques allows measurement of thevoltage difference between the electrode and ground.

[0160] In accordance with an embodiment of the invention, control system800 can perform quantum calculations. Classical driver system 897 inFIG. 11 illustrates an aspect of the invention that can coordinate thetiming of current pulses and voltage measurements, thus interpreting theinformation coming out of quantum register 300 Some embodiments of thecontrol system can include control leads for manipulating the state ofall switches. Such a control system would provide the capacity for theclassical driver system 897 to direct the qubit to be operated on inquantum register 300.

[0161] Quantum computation generally includes initializing a quantumregister to some classical value, performing a sequence of quantum gateoperations on the qubits in the register, and reading out a classicalvalue for the qubits used in the calculation. In accordance with anembodiment of the invention, a quantum register such as quantum register300 of FIG. 11 can perform a quantum computation when combined with acontrol system such as 800 and a classical driver system such as 897 toform a quantum processor 900. The temperature of the system is generallylow enough to suppress thermal excitations. The system can have anenvironment temperature on the order of 10⁻³ Kelvin to 1 Kelvin.Similarly, the classical driver system 897 can run in the sameenvironment as the control system and quantum register. In someembodiments of the invention, the classical driver system 897 can beformed on the same chip as the other aspects of the quantum processor.In another embodiment of the invention, the control system and quantumregister can be at a low enough temperature to perform quantumcomputation, and the classical driver system can run in a separateenvironment, having leads which interface with the control system.

[0162] In some embodiments of the invention, a quantum register mayinclude a plurality of qubits, where each qubit may be coupled to one ormore of the other qubits in the quantum register. FIG. 13 shows aquantum register 600 which includes a plurality of qubit devices 100-1through 100-4 in a two dimensional array. A three dimensional array ofqubit devices may be used as well. Additionally, a larger number ofqubit devices may be used.

[0163]FIG. 13 shows quantum register 600 with four qubit devices 100-1through 100-4 with qubits 113-1 through 113-4. Each qubit may be coupledto any or all of the other qubits in quantum register 600. For example,coupling switches 895-1,2, 895-2,4, 895-3,4, and 895-1,3 shown in FIG.13 may be used to couple qubits as shown here. Coupling switches895-1,2, 895-2,4, 895-3,4, and 895-1,3 may be superconducting SETs orparity keys. Other methods of coupling multiple qubits may be used. Forexample, although FIG. 13 does not show a coupling switch between qubit113-2 and qubit 113-3, such a coupling switch may be provided.

[0164] Although the invention has been described with reference toparticular embodiments, the embodiments specifically described are onlyexamples of the invention's application and should not be taken aslimiting. One skilled in the art will recognize variations that arewithin the spirit and scope of this invention. Various adaptations andcombinations of features of the embodiments disclosed are within thescope of the invention as defined by the following claims.

We claim:
 1. A method of performing a calculation with a quantumcomputer, comprising: providing a plurality of qubit devices including afirst qubit device and a second qubit device, each of said plurality ofqubit devices including a superconducting loop and one or moresuperconducting fingers, said superconducting loop including at leastone Josephson junction, each of said one or more superconducting fingersextending from said superconducting loop towards the interior of saidsuperconducting loop, each of said one or more superconducting fingersfurther including a mesoscopic island separated from the rest of saidsuperconducting finger by a finger Josephson junction; initializing eachof said qubits, including initializing a first qubit and a second qubit;performing a calculation, including performing an entanglement operationon said first qubit and said second qubit; and reading out the result ofthe calculation, including measuring a first qubit value and a secondqubit value.
 2. The method of claim 1, wherein performing anentanglement operation comprises coherently coupling said first qubitdevice to said second qubit device.
 3. The method of claim 1, whereinperforming a calculation further comprises performing a bias operationon said first qubit.
 4. The method of claim 1, wherein performing acalculation further comprises performing a tunnel matrix operation onsaid first qubit.
 5. The method of claim 1, wherein performing anentanglement operation further comprises performing a controlled phaseshift on said first qubit.
 6. The method of claim 1, further comprisingstoring the results of said calculation in a memory, including storingsaid first qubit value in said memory.
 7. The method of claim 1, whereinsaid first qubit device includes a first superconducting loop and afirst mesoscopic island, and wherein measuring said first qubit valueincludes providing a link between said first superconducting loop andsaid first mesoscopic island, providing current through said first qubitdevice, and measuring a voltage across said first qubit device.
 8. Themethod of claim 1, wherein measuring said first qubit value includesproviding current through said first qubit device, and measuring avoltage across said first qubit device.
 9. The method of claim 1,wherein said first qubit device includes a first mesoscopic island, andwherein measuring said first qubit value includes grounding said firstmesoscopic island, providing current through said first qubit device,and measuring a voltage across said first qubit device.
 10. The methodof claim 1, wherein said first qubit device includes a first mesoscopicisland and said second qubit device includes a second mesoscopic islandand wherein performing an entanglement operation on said first qubit andsaid second qubit includes providing a link between said firstmesoscopic island and said second mesoscopic island.
 11. A method ofinitializing a qubit, the method comprising: providing a qubit deviceincluding a qubit, said qubit having two qubit basis states, said qubitdevice comprising a material capable of superconducting, said qubitdevice including a loop and a finger, said loop including at least oneJosephson junction, said finger extending from said loop towards theinterior of said loop, said finger further including a mesoscopic islandseparated from the rest of said finger by a finger Josephson junction,said qubit device further including a first lead and a second leadconfigured to provide current to said loop; and initializing said qubitto one of said two qubit basis states.
 12. The method of claim 11,wherein said qubit includes said finger.
 13. The method of claim 11,wherein initializing said qubit includes connecting said mesoscopicisland of said finger to a ground.
 14. The method of claim 11, whereininitializing said qubit includes connecting said mesoscopic island ofsaid finger to said loop.
 15. The method of claim 14 wherein saidinitializing said qubit further includes driving a bias current acrosssaid first and second leads of said loop.
 16. The method of claim 11,wherein initializing said qubit includes providing a bias currentthrough said first and second leads.
 17. A method for entangling a firstqubit with a second qubit, said method comprising: providing a firstqubit device having a first qubit, said first qubit device including asuperconducting loop and a superconducting finger, said superconductingloop including at least one Josephson junction, said superconductingfinger extending from said superconducting loop towards the interior ofsaid superconducting loop, said superconducting finger further includinga first mesoscopic island separated from the rest of saidsuperconducting finger by a finger Josephson junction; providing asecond qubit device having a second qubit, said second qubit deviceincluding a superconducting loop and a superconducting finger, saidsuperconducting loop including at least one Josephson junction, saidsuperconducting finger extending from said superconducting loop towardsthe interior of said superconducting loop, said superconducting fingerfurther including a second mesoscopic island separated from the rest ofsaid superconducting finger by a finger Josephson junction; and couplingsaid first qubit to said second qubit.
 18. The method of claim 17,wherein coupling said first qubit to said second qubit includesproviding a link between said first mesoscopic island and said secondmesoscopic island.
 19. The method of claim 18, said link between saidfirst mesoscopic island and said second mesoscopic island includes aswitch, and wherein coupling said first qubit to said second qubitincludes closing said switch so that supercurrent can flow between saidfirst mesoscopic island and said second mesoscopic island.
 20. Themethod of claim 19, wherein said switch includes a superconductingsingle electron transistor.
 21. The method of claim 19, wherein saidswitch includes a parity key.
 22. A method of performing a biasoperation on a qubit, said method comprising: providing a qubit deviceincluding a qubit, said qubit device including a superconducting loopand a superconducting finger, said superconducting loop including atleast one Josephson junction, said superconducting finger extending fromsaid superconducting loop towards the interior of said superconductingloop, said superconducting finger further including a mesoscopic islandseparated from the rest of said superconducting finger by a fingerJosephson junction; linking said mesoscopic island to saidsuperconducting loop, wherein said linking is accomplished using acoherent switching mechanism.
 23. The method of claim 22, wherein saidcoherent switching mechanism includes a parity key device.
 24. Themethod of claim 22, wherein said coherent switching mechanism includes asuperconducting single electron transistor device.
 25. A method forperforming a bias operation on a qubit device, said method comprising:providing a qubit device including a qubit, said qubit device includinga superconducting loop and a superconducting finger, saidsuperconducting loop including at least one Josephson junction, saidsuperconducting finger extending from said superconducting loop towardsthe interior of said superconducting loop, said superconducting fingerfurther including a mesoscopic island separated from the rest of saidsuperconducting finger by a finger Josephson junction, said qubit devicefurther including a first lead and a second lead configured to providecurrent to said superconducting loop; and driving a current across saidfirst and second leads.
 26. The method of performing a bias operation ofclaim 25, wherein driving said current across said first and secondleads in a first direction biases said qubit device to a first qubitbasis state and wherein driving said current across said first andsecond leads in a second direction opposite to said first directionbiases said qubit device to a second qubit basis state.
 27. A method ofreading out the state of a qubit, said method comprising: providing aqubit device including a qubit, where said qubit device includes asuperconducting loop having a first lead and a second lead and asuperconducting finger extending toward the interior of said loop, saidsuperconducting finger including a mesoscopic island separated from therest of said finger by a Josephson junction; coupling said mesoscopicisland to said superconducting loop; driving a bias current through saidfirst and second leads; and measuring a voltage across said first andsecond leads.
 28. The method of claim 27, wherein said qubit includessaid finger.
 29. A method of reading out the state of a qubit, saidmethod comprising: providing a qubit device including a qubit, wheresaid qubit device includes a superconducting loop having a first leadand a second lead and a superconducting finger extending toward theinterior of said loop, said superconducting finger including amesoscopic island separated from the rest of said finger by a Josephsonjunction; grounding said qubit; applying a current across said first andsecond leads of said qubit device; and measuring a voltage across saidfirst and second leads of said qubit device.
 30. A method of grounding aqubit, said method including: providing a qubit device including aqubit, where said qubit device includes a superconducting loop and asuperconducting finger extending toward the interior of said loop, saidsuperconducting finger including a mesoscopic island separated from therest of said finger by a Josephson junction; and connecting saidmesoscopic island to a ground.
 31. The method of claim 30, wherein saidqubit includes said superconducting finger.
 32. A method of grounding aqubit, said method including: providing a qubit device including aqubit, where said qubit device includes a superconducting loop having afirst lead and a second lead and a superconducting finger extendingtoward the interior of said loop, said superconducting finger includinga mesoscopic island separated from the rest of said finger by aJosephson junction; and driving current across said first and secondleads.
 33. A method for entangling a plurality of qubits, said methodincluding: providing a plurality of qubit devices, each of said qubitdevices including a superconducting loop having one or moresuperconducting fingers extending toward the interior of said loop, eachof said superconducting fingers including a mesoscopic island separatedfrom the rest of said finger by a Josephson junction, wherein each ofsaid superconducting fingers forms a qubit; and entangling a first qubitwith a second qubit.
 34. The method of claim 33, further includingentangling said first qubit with a third qubit.
 35. The method of claim34, wherein said first qubit is entangled with both said second qubitand said third qubit at a time T.